Question 4 - A-Level Maths

Exam Board	Edexcel
Module	S3 (Statistics 3)
Session	Specimen
Topic	Hypothesis test of Spearman’s rank correlation coefficien

A researcher claims that, at a river bend, the water gradually gets deeper as the distance from the inner bank increases. He measures the distance from the inner bank, \(b \mathrm {~cm}\), and the depth of a river, \(s \mathrm {~cm}\), at seven positions. The results are shown in the table below.

Position	A	B	\(C\)	D	\(E\)	\(F\)	G
Distance from inner bank \(b \mathrm {~cm}\)	100	200	300	400	500	600	700
Depth \(s \mathrm {~cm}\)	60	75	85	76	110	120	104

Calculate Spearman's rank correlation coefficient between \(b\) and \(s\).
Stating your hypotheses clearly, test whether or not the data provides support for the researcher's claim. Use a \(1 \%\) level of significance.